US6433726B1 - Fractional decimation filter using oversampled data - Google Patents

Fractional decimation filter using oversampled data Download PDF

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Publication number
US6433726B1
US6433726B1 US09/887,454 US88745401A US6433726B1 US 6433726 B1 US6433726 B1 US 6433726B1 US 88745401 A US88745401 A US 88745401A US 6433726 B1 US6433726 B1 US 6433726B1
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output
samples
input
decimator
analog
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US09/887,454
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Yiping Fan
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Koninklijke Philips NV
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Koninklijke Philips Electronics NV
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Assigned to KONINKLIJKE PHILIPS ELECTRONICS N.V. reassignment KONINKLIJKE PHILIPS ELECTRONICS N.V. ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: FAN, YIPING
Priority to PCT/IB2002/002336 priority patent/WO2003001669A1/en
Priority to KR10-2003-7002531A priority patent/KR20030027064A/ko
Priority to JP2003507948A priority patent/JP2004521568A/ja
Priority to CNA028123867A priority patent/CN1518794A/zh
Priority to EP02738453A priority patent/EP1405412A1/en
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/06—Non-recursive filters
    • H03H17/0621—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing
    • H03H17/0635—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies
    • H03H17/0642—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies the ratio being arbitrary or irrational
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • H03H17/06—Non-recursive filters
    • H03H17/0621—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing
    • H03H17/0635—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies
    • H03H17/0685—Non-recursive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; Anti-aliasing characterized by the ratio between the input-sampling and output-delivery frequencies the ratio being rational

Definitions

  • This invention relates to the field of digital signal processing, and in particular to the down-sampling or decimation of data at a non-integer, or fractional, sample rate ratio.
  • Sample rate converters are common in the art. Data that is sampled at one rate is converted by a sample rate converter into data that is sampled at a second rate. Down-sampling, or decimation, is used to reduce the sampling rate, and up-sampling, or interpolation, is used to increase the sampling rate. Decreasing a sample rate by a factor of five, for example, can be effected by providing an output sample that corresponds to every fifth input sample. Increasing a sample rate by a factor of five is effected by repeating each input sample five times. Common down-sampling or up-sampling techniques use multiple input samples to generate each output sample.
  • a decimation filter determines the average, or weighted average, of multiple input samples as the output sample value. Additional input samples are often used in the up-sampling process in order to preserve the signal spectrum of the input sample.
  • An interpolation filter provideses the value of each intermediate sample, based on an interpolation, or curve-fitting, of multiple input samples.
  • the ratio F 1 /F 2 can be expressed or approximated as N+P/Q, where N, P, and Q are integers, N being the integer portion of the ratio, and P/Q being the fractional part.
  • oversampling is used to provide highly-accurate analog-to-digital (A/D) conversion, using a technique termed “delta-sigma” conversion.
  • a delta-sigma converter digitizes an analog signal at a very high sampling rate, then filters the samples to remove the noise and interference that is introduced by the sampling process and the communication channel from a transmitter to a receiver, then downsamples the filtered data to the desired sample rate.
  • the oversampling rate, Q, and downsample rate, N*Q+P are selected so as to provide the desired output sampling rate.
  • the oversampling rate and the desired output sampling rate are independently specified, and a fractional downsampling is required. For example, the direct sampling of an intermediate frequency signal often requires that the sampling frequency has certain relation with the intermediate frequency.
  • a decimator that selectively varies the output sampling rate such that the average output sampling rate corresponds to the desired output sampling rate.
  • the output sampling rate varies such that an output sample is provided selectively after N input samples, or after N+1 input samples, to provide an output-to-input sampling ratio that is between N and N+1.
  • This process introduces phase jitter as the sampling frequency varies between 1/N and 1/(N+1), but if the oversampling rate is high, and therefore N is high, as is typical of many applications that employ oversampling, the relative magnitude of the phase jitter is slight.
  • a fractional accumulator is used to control whether the output occurs after N or N+1 input cycles, and is clocked by the input sampling clock, thereby minimizing the complexity of the embodiment.
  • FIG. 1 illustrates an example communications device that includes a fractional decimator in accordance with this invention.
  • FIG. 2 illustrates an example fractional decimator in accordance with this invention.
  • communications systems are commonly designed to sample a received signal at a frequency that is substantially higher than the transmitted data rate.
  • This higher sampling rate allows for proper decoding of the received signal in the presence of noise and/or interference effects as the modulated signal travels from the transmitter to the receiver.
  • the higher sampling frequency is substantially higher than the transmitted data rate, the sampling introduces less quantization noise within the desired signal bandwidth.
  • the higher sampling rate provides multiple samples corresponding to each transmitted data sample, a higher sampling rate facilitates the determination and use of samples corresponding to the best signal to noise ratio, as not every sample along the received analog waveform has the same signal to noise ratio.
  • an analog-to-digital converter with a higher sampling rate also requires fewer bits than a lower sampling rate analog-to-digital converter with the same conversion performance.
  • This invention is premised on the observation that many systems that use a high oversampling analog to digital converters are relatively insensitive to sampling jitter. As discussed below, the additional sampling jitter introduced by the fractional decimation approach in this invention is much less dominant as compared to the sampling phase error.
  • This sampling phase error is the sampling time difference between the actual sampling point and the ideal sampling point within a chip or symbol period, where the maximum signal to noise ratio is realized. The sampling phase error occurs because a communication receiver typically does not know where the ideal sampling point is. Therefore, in an oversampling converter, multiple samples are taken by the analog to digital converter within a symbol or chip period and the sample with the highest SNR is used for further digital processing after the analog to digital conversion.
  • the particular decimation factor that is used to produce each output sample is selectably determined such that the average decimation factor among a stream of output samples corresponds to the desired fractional decimation (albeit thereby introducing phase jitter as different integer decimation factors are selected).
  • the integer decimation factor is selectable from either a value of N to a value of N+1, wherein N is the integer component of the desired output-to-input sampling ratio.
  • N is the integer component of the desired output-to-input sampling ratio.
  • the ratio F 1 /F 2 can be expressed or approximated as N+P/Q, wherein N, P, and Q are integers and Q>P.
  • the input is decimated with a decimation factor of N for (Q ⁇ P) periods and with a decimation factor of N+1 for P periods.
  • the ratio is expressed as 10+4/7.
  • three (Q ⁇ P) output sample are produced at intervals of 10(N) input samples, and four output samples are produced at intervals of 11 (N+1).
  • the late and early samples are interspersed as much as possible.
  • FIG. 1 illustrates an example communications device 100 that includes a fractional decimator 130 in accordance with this invention.
  • sample-rate-conversion is used in a variety of applications, including communications systems, video processing systems, and so on.
  • the communications device 100 is used herein as a paradigm for system that provides oversampled data samples and often requires fractional downsampling to provide filtered data samples at a desired output rate.
  • the fractional downsampling of this invention introduces somewhat more phase jitter than conventional fractional downsamplers, and the communications device 100 is also used as a paradigm of a system that is fairly insensitive to phase jitter.
  • the device 100 is configured to accommodate a plurality of communication standards, thereby allowing it to be used in different geographic regions, depending upon the communication scheme that is available in each region.
  • the device 100 includes a dual band front end 110 that is configured to selectively receive communications from either the PCS frequency band, or the cellular frequency band, and to provide a down-shifted analog signal at a common intermediate frequency (IF) of 183.6 MHz.
  • IF common intermediate frequency
  • the particular frequencies are presented herein as common examples, although the principles of the decimator in accordance with this invention are applicable at any frequencies.
  • Downshifting to a common intermediate frequency is a common technique in the art, to allow subsequent stages to be designed independent of the particular modulation frequency of the received signal, and thereby provide better selectivity and dynamic range.
  • the intermediate frequency (IF) analog signal from the front end 110 is provided to a Quadrature Sigma-Delta analog-to-digital converter (ADC) 150 that is configured to sample the analog signal at a rate that is substantially higher than the required output sample rate, via a quadrature sampler 120 , and to filter the high-sample-rate quadrature input samples, via decimators 130 .
  • ADC Quadrature Sigma-Delta analog-to-digital converter
  • the ADC 150 is configured to support multiple communication standards, including Cellular CDMA (IS-95 A/B), Cellular AMPS, and PCS CDMA (IS-2000 1xRTT).
  • CDMA employs a modulation scheme wherein each data unit (byte, symbol, etc.) is modulated by a selected code-key, and this modulation occurs at a frequency that is termed a “chip-rate”.
  • the received code-key-modulated signal is to be sampled at eight-times the chip-rate, to allow the reliable decoding of each data unit in the presence of sampling phase error.
  • the required output sample rate for CDMA processing is 9.8304 MHz.
  • the chip-rate of the transmitted signal is defined substantially independent of the intermediate sampling rate that used in a particular receiver 100 .
  • the decimators 130 of the Sigma-Delta ADC 150 are configured to provide fractional decimation via the selection of varying integer decimation factors that produce an average output sample rate that corresponds to the desired output rate.
  • the decimation factor is appropriately varied between 9 and 10, corresponding to an average sample ratio of 91.8/9.8304.
  • this desired sample ratio (9.3383789 . . . ) can be achieved in a variety of ways, and in general is achieved by approximating the fractional component to an integer ratio (P/Q) where Q determines the resolution achievable by the approximation.
  • Q is selected to be 8
  • the nearest fraction will be 3 ⁇ 8(0.375).
  • Q is selected to be 2048 (2 11 ).
  • CDMA output sample rate 9.8304 MHz
  • a value of 693 is used for P, thereby providing an average output sample rate of precisely 9.8304 MHz (91.8/(9+693/2048)).
  • the Cellular AMPS signal is provided at a 40 KHz sampling rate, which is an integer multiple of the oversample rate of 91.8 MHz. In this application, all of the samples will be produced at each interval of 2295(N) input samples.
  • any of a variety of techniques may be used to selectively choose integer decimation factors that provide an average decimation ratio that corresponds to the desired output sample rate.
  • the selection need not be limited to N and N+1, but could be combinations, for example, of N ⁇ 1, N, N+1, N+2, or any other combinations.
  • the choice of N and N+1 is preferred so as to minimize the phase jitter as different decimation factors are selected.
  • the N and N+1 intervals are preferably interspersed, so as to minimize the accumulation of phase error as repeated leading or lagging output pulses are produced.
  • the accumulated phase error is contained within +/ ⁇ a half cycle of the input sampling clock, by switching from leading-to-lagging (N to N+1), or lagging-to-leading (N+1 to N), whenever the accumulated phase error would exceed a half cycle if not switched.
  • FIG. 2 illustrates an example fractional decimator 130 in accordance with this invention that limits the phase jitter to +/ ⁇ a half cycle of the input sampling clock.
  • a register 220 contains the determined value of P to achieve a (N+P/Q) sample ratio.
  • a modulo-Q accumulator 230 accumulates successive values of P, and generates an overflow, or carry, signal whenever the accumulated value exceeds Q. If Q is a power of two, the accumulator 230 is merely a conventional accumulator that has a bit width of log 2 (Q). In the example of Q being 2048 (2 11 ), the accumulator 230 is a conventional 11-bit accumulator that overflows whenever the addition of P to the accumulated result exceeds 2048.
  • the overflow signal from the accumulator 230 controls a switch 240 that selectively provides either N or N+1 to an integer decimator 210 .
  • the integer decimator 210 is a conventional “divide-by-K” decimator that provides an output sample at every K occurrences of input samples. In this application, K is selectively N or N+1.
  • the decimator 210 preferably includes a filter function that determines the value of each output sample based on a weighted average of L input samples, so as to minimize noise and interference contribution to the output samples that would occur if only the K th input sample were used as the corresponding output sample.
  • the remainder of the accumulation, modulo Q, is fed back as an input to the accumulator 230 , thereby maintaining a running accumulation of counts.
  • This accumulation of counts corresponds to a measure of the phase difference between the output sample and an ideal output sample that corresponds to the desired output sample rate.
  • the count is reduced (because P ⁇ Q), corresponding to an insertion of a longer-interval (N+1) sample to compensate for the phase shift caused by the shorter-interval (N) sample(s).
  • the output is produced at the (N+1) th input sample, thereby maintaining the phase error within a half cycle of the input sample clock.

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Computer Hardware Design (AREA)
  • Mathematical Physics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Compression, Expansion, Code Conversion, And Decoders (AREA)
  • Digital Transmission Methods That Use Modulated Carrier Waves (AREA)
  • Analogue/Digital Conversion (AREA)
  • Synchronisation In Digital Transmission Systems (AREA)
US09/887,454 2001-06-22 2001-06-22 Fractional decimation filter using oversampled data Expired - Fee Related US6433726B1 (en)

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Application Number Priority Date Filing Date Title
US09/887,454 US6433726B1 (en) 2001-06-22 2001-06-22 Fractional decimation filter using oversampled data
PCT/IB2002/002336 WO2003001669A1 (en) 2001-06-22 2002-06-18 Fractional decimation filter using oversampled data
KR10-2003-7002531A KR20030027064A (ko) 2001-06-22 2002-06-18 오버샘플링된 데이터를 사용하는 분수 데시메이션 필터
JP2003507948A JP2004521568A (ja) 2001-06-22 2002-06-18 オーバーサンプリングされたデータを用いた端数間引きフィルタ
CNA028123867A CN1518794A (zh) 2001-06-22 2002-06-18 使用过采样数据的分数分样滤波器
EP02738453A EP1405412A1 (en) 2001-06-22 2002-06-18 Fractional decimation filter using oversampled data

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Cited By (16)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20030219066A1 (en) * 2001-05-18 2003-11-27 Charles Abraham, Serge De La Porte Method and apparatus for performing signal correlation
US20040032920A1 (en) * 2002-08-14 2004-02-19 Industrial Technology Research Institute. Methods and systems for providing a noise signal
US20040077365A1 (en) * 2001-05-18 2004-04-22 Global Locate Inc. Apparatus for computing signal correlation at multiple resolutions
US20040141549A1 (en) * 2001-05-18 2004-07-22 Charles Abraham Method and apparatus for performing signal correlation using historical correlation data
US20050080494A1 (en) * 2003-10-09 2005-04-14 Melanson John L. Delta sigma modulator with integral decimation
US20060039514A1 (en) * 2004-08-17 2006-02-23 Daniela Radakovic Universal sampling rate converter in electronic devices and methods
US20060114970A1 (en) * 2001-05-18 2006-06-01 Global Locate, Inc. Method and apparatus for performing signal correlation at multiple resolutions to mitigate multipath interference
US20060209935A1 (en) * 2001-05-18 2006-09-21 Global Locate, Inc. Method and apparatus for performing signal processing using historical correlation data
US20070160167A1 (en) * 2006-01-09 2007-07-12 May Michael R Integrated circuit having radio receiver and methods for use therewith
US20080186217A1 (en) * 2007-02-06 2008-08-07 Lei Chen Low pin count high speed interface for video and audio codec applications
US20090079598A1 (en) * 2007-09-20 2009-03-26 Kabushiki Kaisha Toshiba Sample rate converter
US20130156141A1 (en) * 2011-12-14 2013-06-20 Electronics And Telecommunications Research Institute Digital radio frequency (rf) receiver
US8472503B2 (en) 2003-10-22 2013-06-25 Global Locate, Inc. Method and apparatus for performing frequency synchronization
CN104218919A (zh) * 2014-09-15 2014-12-17 中国电子科技集团公司第三十八研究所 一种分数倍内插成型滤波器及其实现方法
EP2676489A4 (en) * 2011-02-18 2016-12-07 Pc-Tel Inc SYSTEM AND METHOD FOR ACQUIRING DATA OF A NETWORK
US10119996B2 (en) 2014-03-25 2018-11-06 Eaton Intelligent Power Limited Data decimation system and method for facilitating transmission and viewing of waveforms generated by an electrical device

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Cited By (30)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8411726B2 (en) 2001-05-18 2013-04-02 Global Locate, Inc. Method and apparatus for performing signal correlation at multiple resolutions to mitigate multipath interference
US20040077365A1 (en) * 2001-05-18 2004-04-22 Global Locate Inc. Apparatus for computing signal correlation at multiple resolutions
US20030219066A1 (en) * 2001-05-18 2003-11-27 Charles Abraham, Serge De La Porte Method and apparatus for performing signal correlation
US20040141549A1 (en) * 2001-05-18 2004-07-22 Charles Abraham Method and apparatus for performing signal correlation using historical correlation data
US8170086B2 (en) 2001-05-18 2012-05-01 Global Locate, Inc. Method and apparatus for performing signal correlation
US7995682B2 (en) 2001-05-18 2011-08-09 Broadcom Corporation Method and apparatus for performing signal processing using historical correlation data
US20060114970A1 (en) * 2001-05-18 2006-06-01 Global Locate, Inc. Method and apparatus for performing signal correlation at multiple resolutions to mitigate multipath interference
US20060209935A1 (en) * 2001-05-18 2006-09-21 Global Locate, Inc. Method and apparatus for performing signal processing using historical correlation data
US7184464B2 (en) * 2001-05-18 2007-02-27 Global Locate, Inc Apparatus for computing signal correlation at multiple resolutions
US7190712B2 (en) 2001-05-18 2007-03-13 Global Locate, Inc Method and apparatus for performing signal correlation
US7672358B2 (en) 2001-05-18 2010-03-02 Broadcom Corporation Method and apparatus for performing signal correlation at multiple resolutions to mitigate multipath interference
US20070160121A1 (en) * 2001-05-18 2007-07-12 Global Locate, Inc. Method and apparatus for performing signal correlation
US7567636B2 (en) 2001-05-18 2009-07-28 Global Locate, Inc. Method and apparatus for performing signal correlation using historical correlation data
US7251301B2 (en) * 2002-08-14 2007-07-31 Industrial Technology Research Institute Methods and systems for providing a noise signal
US20040032920A1 (en) * 2002-08-14 2004-02-19 Industrial Technology Research Institute. Methods and systems for providing a noise signal
US7212137B2 (en) * 2003-10-09 2007-05-01 Cirrus Logic, Inc. Delta sigma modulator with integral decimation
US20050080494A1 (en) * 2003-10-09 2005-04-14 Melanson John L. Delta sigma modulator with integral decimation
US8989236B2 (en) 2003-10-22 2015-03-24 Global Locate, Inc. Method and apparatus for performing frequency synchronization
US8472503B2 (en) 2003-10-22 2013-06-25 Global Locate, Inc. Method and apparatus for performing frequency synchronization
US20060039514A1 (en) * 2004-08-17 2006-02-23 Daniela Radakovic Universal sampling rate converter in electronic devices and methods
US8130871B2 (en) * 2006-01-09 2012-03-06 Sigmatel, Inc. Integrated circuit having radio receiver and methods for use therewith
US20070160167A1 (en) * 2006-01-09 2007-07-12 May Michael R Integrated circuit having radio receiver and methods for use therewith
US20080186217A1 (en) * 2007-02-06 2008-08-07 Lei Chen Low pin count high speed interface for video and audio codec applications
US20090079598A1 (en) * 2007-09-20 2009-03-26 Kabushiki Kaisha Toshiba Sample rate converter
EP2676489A4 (en) * 2011-02-18 2016-12-07 Pc-Tel Inc SYSTEM AND METHOD FOR ACQUIRING DATA OF A NETWORK
US20130156141A1 (en) * 2011-12-14 2013-06-20 Electronics And Telecommunications Research Institute Digital radio frequency (rf) receiver
US9294135B2 (en) * 2011-12-14 2016-03-22 Electronics And Telecommunications Research Institute Digital radio frequency (RF) receiver
US10119996B2 (en) 2014-03-25 2018-11-06 Eaton Intelligent Power Limited Data decimation system and method for facilitating transmission and viewing of waveforms generated by an electrical device
CN104218919A (zh) * 2014-09-15 2014-12-17 中国电子科技集团公司第三十八研究所 一种分数倍内插成型滤波器及其实现方法
CN104218919B (zh) * 2014-09-15 2017-05-03 中国电子科技集团公司第三十八研究所 一种分数倍内插成型滤波器及其实现方法

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KR20030027064A (ko) 2003-04-03

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